Magnetar Spin-Down Energy as a Cap on Gamma-Ray Burst Plateau Luminosities

Many gamma-ray burst afterglows show a plateau that a newborn magnetar could power. The model is testable because rotation provides a hard energy ceiling: no plateau can radiate more than the rotational energy of the remnant. This paper computes rotational energies, initial spin-down luminosities and spin-down times across the plausible period and field range. Using the calculation described in the Methods, the headline results are: Erot_P1ms_erg = 2e+52, L0_B1_P1 = 1e+49, t_sd_typical_s = 2000, Erot_P0p7ms_erg = 4.08e+52. A millisecond magnetar stores about 2 x 10^52 erg, comfortably above plateau radiated energies after beaming and efficiency corrections for most events, but a minority of very bright plateaus press against the cap and would require periods below the breakup limit. Those events are therefore better explained by continued accretion. The cap thus sorts the plateau population rather than merely accommodating it. This study is simulated and computed from stated assumptions; it is not a measurement. All headline numbers in this abstract appear in the deposited results file and are reproduced by running the deposited code without modification.